通过Word实现曲线和前沿的不变量
Invariants via word for curves and fronts
摘要：
利用V.Turaev提出的字理论，构造了曲面中曲线的无穷序列不变量。对于平面闭曲线，我们添加一些额外的项，例如旋转数。从这些修正的不变量中，我们得到了Arnold的基本不变式和其他一些不变量。我们还表达了这些不变量如何分类平面闭曲线。此外，我们考虑其他类别的平面曲线：长曲线和前线。
英文摘要：
We construct the infinite sequence of invariants for curves in surfaces by using word theory that V. Turaev introduced. For plane closed curves, we add some extra terms, e.g. the rotation number. From these modified invariants, we get the Arnold's basic invariants and some other invariants. We also express how these invariants classify plane closed curves. In addition, we consider other classes of plane curves: long curves and fronts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
